Treatment of Deterred Propellants in
Interior Ballistic Calculations
Dejan Micković
Associate Professor
University of Belgrade
Faculty of Mechanical Engineering
In the paper the procedure for determination of deterred propellant
characteristics that are necessary as input parameters in interior ballistic
calculations is given. The basic features of developed model for interior
ballistic cycle calculation of systems with deterred propellant propelling
charge are presented. The model verification is carried out through
comparison of computational results with American experimental data of
20 mm rounds with ball propellant propelling charge.
Keywords: interior ballistics, propellant, propelling charge, deterrent.
1. INTRODUCTION
In modern interior ballistic practice it is often required
to design such a propelling charge that will provide
practically maximum performance to the given gunprojectile system. The character of existing limitations
usually imposes the requirement for very high
progressivity of propellant combustion.
The possibilities are limited to obtain specific
favourable rate of propellant gas formation during
interior ballistic cycle only by the variation of propellant
grain geometry. Therefore, the required combustion
progressivity if often provided by the use of chemically
modified (deterred) propellants.
The existing interior ballistic models are incapable to
treat adequately the combustion of deterred propellants.
Therefore, these models are practically useless in many
cases where sophisticated design of high performance
propelling charge is required. That is why the new
interior ballistic model is developed for propelling
charges composed of deterred propellants. The main
particularities of the developed model will be presented
here; the special attention will be paid to the specific
case of ball propellants combustion. The procedure for
determination of deterred propellant characteristics,
which are necessary as input parameters for interior
ballistic calculations, will also be considered.
The penetration depth of deterrent, its chemical
identity, and its concentration level in the propellant
characterise the deterred region from the chemical point
of view for purposes of interior ballistic calculations.
The reason that the penetration depth and the
concentration of deterrent in the total propellant
composition are considered sufficient to chemically
characterise the deterred layer is due to the special
shape of the concentration profile of the deterrent in
propellant grains.
2. CHARACTERISTICS OF DETERRED
PROPELLANTS
The deterrent concentration profile has been
experimentally determined. The concentration profile
Received: May 2010, Accepted: June 2010
Correspondence to: Dr Dejan Micković
Faculty of Mechanical Engineering,
Kraljice Marije 16, 11120 Belgrade 35, Serbia
E-mail: [email protected]
© Faculty of Mechanical Engineering, Belgrade. All rights reserved
shape for the case of dibutyl phthalate (DBP)
penetration in the ball propellant grain is presented in
Figure 1 [1].
Figure 1. Deterrent concentration profile in the spherical
propellant grain
The figure shows the shape of a diffusion front of a
given plastisizer into a polymer matrix. This shape
indicates that the deterrent concentration is nearly
constant in the deterred layer and decreases sharply at
the boundary line between deterred and undeterred
regions. The consequence of a square-wave deterrent
concentration profile is that one can assume a constant
level of deterrent in the deterred region and that all of
the deterrent in the propellant is evenly distributed
through the deterred region (step function). The mean
penetration depth of deterrent eD is a mean distance
from the propellant grain surface to the boundary
between the deterred region and the grain interior where
there is almost no deterrent.
In the case of propellants with nonuniform particle
size, such as ball propellants, the propellant granulation
must be known to make possible the determination of
the mass fraction of propellant grain deterred layer.
FME Transactions (2010) 38, 137-141 137
The granulation of WC 870 (lot A.L. 45137)
unrolled ball propellant is given in Table 1, where φi is
the propellant mass fraction retained at i-th sieve and di
is the i-th sieve hole diameter.
Table 1. Granulation of WC 870 (lot A.L. 45137) propellant
φi
Sieve No.
di [mm]
dm,i [mm]
U.S. # 16
0.0000
1.197
# 18
0.0324
1.003
1.100
# 20
0.3275
0.841
0.922
# 25
0.5214
0.707
0.774
# 30
0.1051
0.595
0.651
Ingredient
# 35
0.0102
0.500
0.548
# 40
0.0021
0.420
0.460
Nitrocellulose
(% of nitrogen)
79.70
(13.11)
PAN
0.0094
0.354
0.387
Table 2. Overall chemical composition of WC 870 (lot A.L.
45137) propellant with deterred and undeterred layers
composition
In the case of constant propellant density
(nitroglycerine is assumed to be uniformly distributed
throughout the grain) the deterred layer mass fraction of
unrolled ball propellant is defined by the following
expression:
MD = 1 −
n−1
(
φ1( d1 − 2eD ) + ∑ φ i dm,i − 2eD
3
−
The chemical composition of WC 870 (lot A.L.
45137) spherical ball propellant is given in the left
column of Table 2. The moisture (water) and residual
solvent (ethyl acetate) have been arbitrarily taken to be
equal to one-half of the total volatiles (1.26 %). The
compositions of deterrent-containing and undeterred
regions calculated by (2), (3) and (4) are presented in
the middle and right column of Table 2.
i =2
)
3
3
+ φ n( dn − 2eD )
(1)
n−1
3
3
φ1d13 + ∑ φ i dm,
i + φ n dn
1
Xi = Si ⋅
1 − SD
(2)
where Si is the i-th component mass fraction in the
propellant and SD is deterrent mass fraction in the
propellant.
The deterred layer of propellant grain contains all
the deterrent, and consequently the deterrent mass
fraction in this region is:
YD =
SD
.
MD
(3)
The mass fractions of other components in deterred
layer are proportionate to the mass fractions of
corresponding components in undeterred layer of
propellant grain. So, the i-th component mass fraction in
deterred layer is:
Yi = Xi ⋅ (1 − SD ) .
138 ▪ VOL. 38, No 3, 2010
(4)
71.89
(13.11)
84.13
(13.11)
9.72
Nitroglycerine
9.21
8.31
Dibutyl phthalate
5.27
14.55
0.00
Dinitrotoluene
0.64
0.58
0.68
Diphenylamine
0.88
0.79
0.93
Water
0.63
0.57
0.67
Ethyl acetate
0.63
0.57
0.67
Graphite
0.10
0.09
0.11
Potassium nitrate
0.78
0.70
0.82
Calcium carbonate
0.79
0.71
0.83
Sodium sulfate
0.19
0.17
0.20
Tin dioxide
i =2
where dm,i = (di + di-1)/2 and φn is the propellant mass
fraction passed through the finest sieve.
The assumption of constant propellant grain density
represents certain deviation from real conditions.
However, this assumption is fully acceptable in interior
ballistic calculations.
For given WC 870 propellant granulation and
measured mean deterrent penetration depth eD = 0.056 mm
the deterred layer mass fraction MD = 0.3621 is obtained.
When propellant chemical composition is known, the
i-th component mass fraction in undeterred layer of
propellant grain (Xi) is given by the following expression:
Overall
Deterred Undeterred
composition [%] layer [%] layer [%]
1.18
1.07
1.25
100.00
100.00
100.00
Thermochemical properties associated with the
compositions given in Table 2 were calculated with the
TCC (ThermoChemical Calculations) code [2]. The
results of thermochemical calculations for the charge
density 0.2 g/cm3 are given in Table 3.
Table 3. WC 870 (lot A.L. 45137) thermochemical
3
characteristics (TCC code, ∆ = 0.2 g/cm )
Characteristic
Overall
composition
Deterred
layer
Undeterred
layer
Flame
temperature [K]
Tc;
2750
T1,c;
1978
T2,c;
3189
Covolume
[m3/kg]
α;
0.930 ⋅ 10-3
α1;
0.981 ⋅ 10-3
α2;
0.907 ⋅ 10-3
Specific heats
ratio
κ;
1.241
κ1;
1.266
κ2;
1.227
Molar mass
[g/mol]
µ;
23.947
µ1;
21.204
µ2;
25.865
Propellant
force* [J/kg]
f;
954800
f1;
775600
f2;
1025100
*f =
ℜ
-1 -1
⋅ T ; ℜ – universal gas constant (8.3144 J mol K )
µ c
The linear burning rate of propellants as a function
of pressure is commonly described for interior ballistic
calculations by an equation of the form r = apn + b.
Experience has indicated that the linear burning rate of
propellant increases with the flame temperature. This
observation led to suggestions for empirical correlations
between the flame temperature of propellant
compositions and their burning law coefficients (a, b
and n) in the equation r = apn + b.
FME Transactions
From the calculated flame temperatures of deterredcontained and undeterred layer of propellant grain
(Table 3) the burning rate coefficients of these layers
can be determined by the use of empirical correlations.
Three correlations were used in this study as follows (r
[mm/s]; p [MPa]):
• Muraour [3]:
r = 0.078 ⋅ e
•
0.709(Tc 1000 )
p + 0.5 ,
(5)
Goldstein [4]:
−4
r = 827.76 ⋅ e−8.15+8.62⋅10 Tc p 0.7 ,
•
for the burned distance of propellant grain equal to the
deterrent penetraion depth (e = eD).
The combustion process of deterred propellant can
be divided in two phases.
In the first phase only the deterred layer combustion
takes place. This phase lasts as long as e ≤ eD, that is
0 < z < zD .
The Noble-Abel equation of state for propellant
gases originated from the deterred layer combustion
is:
ωz
(6)
p=
W0 + s X −
Riefler i Lowery [5]:
(
)
r = 8.3956 ⋅10−4 Tc − 0.834 p 0.8053 .
(7)
A survey of calculated coefficients a, b and n in the
r = apn + b burning law for overall composition,
deterred and undeterred layer of WC 870 (lot A.L.
45137) propellant is given in Table 4.
Table 4. Parameters a, b and n in WC 870 (lot A.L. 45137)
n
propellant burning law r = ap + b (p [bar], r [m/s])
a ⋅ 104 b ⋅ 104
Miraour
Goldstein
Riefler &
Lowery
n
Overall composition
0.548
5.0
1.0
Deterred layer
0.317
5.0
1.0
Undeterred layer
0.748
5.0
1.0
Overall composition
5.104
0
0.7
Deterred layer
2.624
0
0.7
Undeterred layer
7.452
0
0.7
Overall composition
2.309
0
0.8053
Deterred layer
1.294
0
0.8053
Undeterred layer
2.886
0
0.8053
d ( e e0 )
dt
=
(
1
a1 ⋅ p n1 + b1
e0
⎛
ω z ⎜ f1 −
⎝
(8)
where: e0 is half of the initial web of propellant grain, e
is burned distance of propellant grain, p is mean
(ballistic) pressure of propellant gas, t is time and a1, b1
and n1 are coefficents in deterred layer burning law
(Table 4).
The mass fraction of burned propellant is defined by
the propellant grain form function:
2
⎛ e ⎞
⎛ e ⎞
⎛ e ⎞
z = ff1 ⎜ ⎟ + ff 2 ⎜ ⎟ + ff3 ⎜ ⎟
⎝ e0 ⎠
⎝ e0 ⎠
⎝ e0 ⎠
3
(9)
where ff1, ff2 i ff3 are the form function coefficients.
The mass fraction of burned propellant at the end of
the deterred layer combustion (zD) is obtained from (9)
FME Transactions
ℜ ⎞
T⎟
µ1 ⎠
( κ1 − 1)
=
1
ϕ mprV 2
2
(11)
where: f1 is force of propellant deterred layer, κ1 is
specific heats ratio of gas (cp/cv) from deterred layer
combustion, mpr is projectile mass, φ is coefficient of
projectile fictitious mass and V is projectile velocity.
Combining (10) and (11) the following expression is
obtained for mean (ballistic) gas pressure:
p=
)
(10)
ω
(1 − z ) − ω zα1
ρ
where: T is mean temperature of propellant gas, ω is
propellant charge mass, W0 is propellant chamber
volume, s is gun tube cross-sectional area, X is
projectile displacement, ρ is propellant density, µ1 is
molar mass of propellant gas from deterred layer
combustion and α1 is covolume of propellant gas from
deterred layer combustion.
The energy equation in this phase of propellant
combustion is:
3. INTERIOR BALLISTIC MODEL
The linear burning rate of propellant is usually
expressed as a change in time of a burned distance of
propellant grain (r = de/dt). Thus, the following
expression holds during combustion of deterred layer of
propellant grain:
ℜ
T
µ1
ω z f1 −
κ1 − 1
ϕmprV 2
2
ω
W0 + s X − (1 − z ) − ω zα1
ρ
.
(12)
In the developed interior ballistic model the equation
(12) is used for gas pressure calculation at each
integration step of differential equations.
Equation (12) is identical in form with equation
used in lumped parameters interior ballistic models for
propellant
charges
composed
of
undeterred
propellants.
The second phase of propellant combustion starts at
the moment when combustion of deterred layer is
terminated (e = eD; z = zD). In this phase only the
combustion of undeterred layer occurs, creating behind
a projectile the mixture of deterred and undeterred layer
combustion products. The composition of this mixture is
different at each moment. Mass fraction of burned
propellant is zD < z < 1 .
Equation of state of mixture is:
p=
ω zD
W0 + s X −
ℜ
ℜ
T + ω ( z − zD ) T
µ1
µ2
ω
(1 − z ) − ω z Dα1 − ω ( z − z D ) α 2
ρ
. (13)
VOL. 38, No 3, 2010 ▪ 139
Energy equation is:
⎛
ω z D ⎜ f1 −
ℜ ⎞
T⎟
µ1 ⎠
⎝
( κ1 − 1)
⎛
ω ( z − zD ) ⎜ f2 −
⎝
+
( κ2 − 1)
ℜ ⎞
T⎟
µ2 ⎠
=
+
1
ϕ mprV 2 .
2
(14)
In order to combine (13) and (14) by elimination of
temperature T, the principle of mixture of deterred and
undeterred propellant layer combustion products is
introduced. At each moment of the combustion process
the propellant force of instantaneous mixture (f*) is
given by the following relation:
ω z f * = ω z D f1 + ω ( z − z D ) f 2 .
(15)
Propellant force, covolume and specific heats ratio
of gaseous mixture are defined by expressions:
f* =
zD
⎛ z ⎞
f1 + ⎜ 1 − D ⎟ f 2
z
z ⎠
⎝
z
⎛ z ⎞
α = D α1 + ⎜1 − D ⎟ α 2
z
z ⎠
⎝
z
⎛ z ⎞
κ* = D κ1 + ⎜1 − D ⎟ κ 2 .
z
z ⎠
⎝
*
(16)
The mean pressure of propellant gas mixture is now
given by equation equivalent to (12), but with
instantaneous mixture characteristics f*, α* and κ*.
Finally, the gas pressure is defined by the following
expression:
p=
ω z D f1 + ω ( z − z D ) f 2 −
W0 + s X −
κ* − 1
ϕ mprV 2
2
ω
(1 − z ) − ω zα1 − ω ( z − z D ) α 2
ρ
. (17)
Equation (17) is also valuable after completion of
propellant combustion, with z = 1 and with constant
value of κ* obtained from (16) for z = 1.
The PERFFL code for the computation of whole
interior-ballistic cycle of ammunition whose propellant
charge is composed of deterred propellant is created.
The model verification is carried out by comparison
with American experimental results of 20 mm M55A2
ammunition firings from 20 mm D20 gun [6]. The
propellant charge of this ammunition consists of WC
870 ball propellant.
In existing lumped parameters interior ballistic model
(GRAD code) and in PERFFL code the grain geometry
of a given ball propellant is expressed as the equivalent
(S )
mean diameter deq
based on particle surface area. The
equivalent mean diameter is calculated from the
following equation with the particle size distribution
obtained from a sieve analysis of the propellant.
n −1
(S )
2
2
deq
= φ1d12 + ∑ φ i d m,
i + φ n dn .
2
140 ▪ VOL. 38, No 3, 2010
(18)
The SFERFL computer code is created in order to
achieve more adequate treatment of ball propellant
combustion. In this code the combustion of each
granulation is considered separately in such a way that
i-th granulation is represented as a ball propellant with
mean grain diameter dm,i.
In Table 5 the comparison of computational results
of the main interior ballistic parameters (projectile
muzzle velocity – V0, maximum ballistic pressure – pm)
with experimental data is given. The WC 870 ball
propellant characteristics (force, covolume, specific
heats ratio, burning law) given in Tables 3 and 4 were
used for interior ballistic calculations (burning law
coefficients according to Miraour).
Table 5. Comparison of computational results for main IB
parameters with experimental data
V0 [m/s]
pm [bar]
Experiment
1045
2950
GRAD code
1051
5694
PERFFL code
1047
3228
SFERFL code
1036
3080
From Table 5 it is clear that GRAD code treat
inadequately the deterred propellant combustion. It was
not possible to obtain computational results close enough
to the experimental data by the input parameters variations
within the wide limits of physically realistic values.
Computational results similar to corresponding
experimental data were obtained with PERFFL and
SFERFL codes at the very start. The similarity of results
was easily attained in both cases by the convenient
adjustment of input parameters (“lumped parameters”
models).
It seems that SFERFL code has not an appreciable
advantage over PERFFL code in estimations of main
interior ballistic parameters. This indicates that the
treatment of ball propellant combustion by the
equivalent mean diameter based on particle surface area
is quite satisfactory in most cases.
The SFERFL code is expected to show significant
advantages during considerations of such practical
interior ballistic problems where the whole curve of
pressure changes in time is important.
4. CONCLUSIONS
Based on previous considerations, the following
conclusions can be drawn:
• The deterred layer characteristics of propellant
grain must be taken into consideration in interior
ballistic calculations for successful design of
high performance propelling charges. Existing
interior ballistic models are incapable to treat
adequately the combustion of deterred
propellants;
• The new model is developed for interior ballistic
cycle calculations of systems with propelling
charge composed of deterred propellants. The
special version of computer code is also created
for calculations of ball propellants combustion;
• The procedure is defined for determination of
deterred propellants characteristics, which are
FME Transactions
•
necessary
for
interior
ballistic
cycle
calculations;
The verification of developed models is carried
out through the comparison with American
experimental data of 20 mm ammunition with
propellant charge composed of deterred ball
propellant.
[5] Riefler, D.W. and Lowery, D.J.: Linear Burn Rates
of Ball Propellants Based on Closed Bomb Firings,
Olin Corporation, Clayton, Missouri, 1974.
[6] Dillon Jr., R.E. and Nagamatsu, H.T.: An
Experimental Study of Perforated Muzzle Brakes,
Large Caliber Weapon Systems Laboratory,
Watervliet, 1984.
REFERENCES
[1] Stiefel, L.: Thermochemical and Burning Rate
Properties of Deterred U.S. Small Arms
Propellants, Fire Control and Small Caliber
Weapon Systems Laboratory, Dover, New Jersey,
1980.
[2] Micković, D. and Jaramaz, S.: TCC – Computer
Code for Thermo Chemical Calculations, Faculty
of Mechanical Engineering, University of Belgrade,
Belgrade, 1996, (in Serbian).
[3] Grollman, B.B. and Nelson, C.W.: Burning rates of
standard army propellants in strand burner and
closed chamber tests, in: Proceedings of the 13th
JANNAF Combustion Meeting (CPIA Publication
381), 09.1976, Monterey, USA, pp. 21-43.
[4] Goldstein, S.: A Simplified Model for Predicting the
Burning Rate and Thermochemical Properties of
Deterred Rolled Ball Propellant, Frankford
Arsenal, Philadelphia, 1973.
FME Transactions
ТРЕТИРАЊЕ ФЛЕГМАТИЗОВАНИХ БАРУТА
У УНУТРАШЊЕБАЛИСТИЧКИМ
ПРОПАЧУНИМА
Дејан Мицковић
У раду је дат поступак одређивања карактеристика
флегматизованог барута које су неопходне као
улазни
параметри
за
унутрашњебалистичке
прорачуне. Приказане су основне специфичности
развијеног
модела
за
прорачун
унутрашњебалистичког
циклуса
система
са
барутним пуњењем од флегматизованог барута.
Верификација модела извршена је упоређењем
прорачунских
резултата
са
америчким
експерименталним резултатима опаљења муниције
калибра 20 mm са барутним пуњењем од сферичног
барута.
VOL. 38, No 3, 2010 ▪ 141